Estimating Prevalence Correctly

Complex Sampling in National Surveys

Mohd Azmi Bin Suliman

azmi.suliman@moh.gov.my

Pusat Penyelidikan Penyakit Tak Berjangkit, Institut Kesihatan Umum

Sunday, 16 November 2025

Institutes for Public Health (Institut Kesihatan Umum - IKU)

Who are we?

National Health Surveys: Conducts large-scale surveys like NHMS to monitor Malaysia’s population health.
Public Health Research: Focuses on epidemiology, including non-communicable diseases, nutrition, communicable diseases, both among the general population and specific age groups.
Policy Support: Provides data-driven evidence to guide national health planning and interventions.

What we do?

NHMS Reports

https://iku.nih.gov.my/nhms

Samples vs. Population

The Sampling Problem

In describing a population, we often use a handful of samples rather than the whole population.
Unfortunately, sample distribution may differ from the population - gender, ethnicity, age.
Small studies typically limit their sample; clearly define the target population using inclusive and exclusive criteria.
But national surveys, including health surveys, require the sample to represent the general population (e.g., adult population, older person population, maternal and child population).

Malaysian Population

This is the Malaysian population pyramid.
Source: https://open.dosm.gov.my/data-catalogue/population_malaysia

The codes

pacman::p_load(tidyverse, arrow)

pyr_df <- read_parquet("https://storage.dosm.gov.my/population/population_malaysia.parquet") %>%
  filter(date == as.Date("2025-01-01"), sex %in% c("male", "female"), 
         age != "overall", ethnicity == "overall") %>%
  mutate(pop_k = population, pop = if_else(sex == "male", -pop_k, pop_k), 
         age0 = readr::parse_number(age), age = fct_reorder(age, age0))

my_pyr_plot <- ggplot(pyr_df, aes(x = age, y = pop, fill = sex)) + 
  geom_col(width = 0.9) + coord_flip() +
  scale_y_continuous(limits = c(-2000, 2000), breaks = seq(-2000, 2000, 500), 
                     labels = function(x) scales::comma(abs(x)), 
                     expand = expansion(mult = c(0.02, 0.02))) +
  labs(title = "Malaysia Population Pyramid, 2025", x = "Age group (years)", 
       y = "Population (thousands)", fill = "Sex") +
  theme_minimal(base_size = 13) + theme(panel.grid.minor = element_blank())

my_pyr_plot

Complex Sampling

What is Complex Sampling?

Structured selection – Instead of simple random sampling, respondents are chosen through stratified and clustered sampling to ensure representation across diverse groups.
Unequal probabilities – Some groups are oversampled (e.g., small states, older adults) to obtain reliable estimates, necessitating the use of sampling weights to correct for these differences.
Design-based inference – Analysis must account for the survey’s design, including strata, clusters, and weights,so that standard errors and prevalence estimates accurately reflect the true population.

Why Complex Sampling?

Sampling: We use a sample to estimate the population efficiently, saving time, cost, and resources while still capturing key characteristics.
Stratification: Stratifying (by gender, ethnicity) ensures all important subgroups are represented and improves precision of estimates.
Clustering: Clustering respondents by area makes data collection logistically practical and cost-efficient.

Example - Diabetes among Malaysian (NHMS 2023)

Category	Overall %	95% CI	Male %	95% CI	Female %	95% CI
Malaysia	15.6	14.4–16.9	15.0	13.6–16.5	16.2	14.7–18.0
Age Group
18–29	3.2	2.2–4.6	3.7	2.2–6.1	2.6	1.7–4.1
30–39	6.5	5.2–8.1	6.9	5.0–9.3	6.0	4.5–7.9
40–49	15.2	13.2–17.4	13.7	11.1–16.8	16.8	14.2–19.8
50–59	28.8	25.0–33.0	28.4	24.2–33.0	29.3	24.4–34.7
60+	38.0	35.4–40.7	37.7	34.0–41.5	38.4	35.0–41.8
Ethnicity
Malay	16.2	15.1–17.4	15.5	14.1–17.1	16.9	15.4–18.4
Chinese	15.1	11.6–19.5	14.8	11.2–19.3	15.5	11.0–21.3
Indian	26.4	22.1–31.2	28.4	22.1–35.7	24.5	19.4–30.4
B. Sabah	9.3	7.3–11.8	9.5	6.8–13.0	9.1	6.5–12.6
B. Sarawak	17.2	13.0–22.3	14.9	10.4–21.0	19.3	14.3–25.6
Others	10.2	7.5–13.6	10.0	6.6–14.8	10.6	6.4–17.0

Simulation

Raw dataset need permission, so we will simulate here.
The simulated dataset can be obtain from github site.
https://github.com/MohdAzmiSuliman/MyRUG_ComplexSamplingNHMS
In this simulation, we assumed that our sample had 1,100 respondent.
- 200 for each 18-29 yo, 30-39 yo, 40-49 yo, 50-59 yo and 300 for 60+ yo
- 40/60 ratio for male/female
- 65/20/15 ratio for malay/chinese/indian
- the proportion of dm is almost similar to the NHMS findings.

# A tibble: 30 × 6
# Groups:   age_group, gender [10]
   age_group gender ethnicity     n dm_prev  n_dm
   <chr>     <chr>  <chr>     <int>   <dbl> <int>
 1 18-29     male   chinese      16    6.25     1
 2 18-29     male   indian       12    8.33     1
 3 18-29     male   malay        52    3.85     2
 4 18-29     female chinese      24    4.17     1
 5 18-29     female indian       18    5.56     1
 6 18-29     female malay        78    2.56     2
 7 30-39     male   chinese      16    6.25     1
 8 30-39     male   indian       12    8.33     1
 9 30-39     male   malay        52    7.69     4
10 30-39     female chinese      24    4.17     1
# ℹ 20 more rows

# A tibble: 10 × 5
# Groups:   age_group [5]
   age_group gender     n dm_prev  n_dm
   <chr>     <chr>  <int>   <dbl> <int>
 1 18-29     male      80    5        4
 2 18-29     female   120    3.33     4
 3 30-39     male      80    7.5      6
 4 30-39     female   120    6.67     8
 5 40-49     male      80   15       12
 6 40-49     female   120   18.3     22
 7 50-59     male      80   31.2     25
 8 50-59     female   120   31.7     38
 9 60+       male     120   40       48
10 60+       female   180   41.7     75

# A tibble: 5 × 4
  age_group     n dm_prev  n_dm
  <chr>     <int>   <dbl> <int>
1 18-29       200     4       8
2 30-39       200     7      14
3 40-49       200    17      34
4 50-59       200    31.5    63
5 60+         300    41     123

# A tibble: 1 × 3
      n dm_prev  n_dm
  <int>   <dbl> <int>
1  1100      22   242

The codes

tibble(age_group = c("18-29","30-39","40-49","50-59","60+"), 
       n_total = c(200, 200, 200, 200, 300)) %>% 
  mutate(male = as.integer(round(.4*n_total)), 
         female = n_total - male) %>% 
  pivot_longer(male:female, names_to = "gender", values_to = "n_gender") %>% 
  mutate(malay = as.integer(round(.65*n_gender)), 
         chinese = as.integer(round(.2*n_gender)), 
         indian = n_gender - malay - chinese) %>% 
  pivot_longer(malay:indian, names_to = "ethnicity", values_to = "n_ethnic") %>% 
  uncount(n_ethnic) %>% 
  select(-starts_with("n_")) %>% 
  group_by(age_group) %>% 
  mutate(age = case_when(age_group == "18-29" ~ sample(18:29, n(), replace = T))) %>% 
  ungroup() %>% 
  mutate(dm = c(rep(0, 50), rep(1, 2), rep(0, 15), rep(1, 1), rep(0, 11), rep(1, 1), 
                rep(0, 76), rep(1, 2), rep(0, 23), rep(1, 1), rep(0, 17), rep(1, 1), 
                rep(0, 48), rep(1, 4), rep(0, 15), rep(1, 1), rep(0, 11), rep(1, 1), 
                rep(0, 73), rep(1, 5), rep(0, 23), rep(1, 1), rep(0, 16), rep(1, 2), 
                rep(0, 45), rep(1, 7), rep(0, 14), rep(1, 2), rep(0, 9), rep(1, 3), 
                rep(0, 65), rep(1, 13), rep(0, 20), rep(1, 4), rep(0, 13), rep(1, 5), 
                rep(0, 37), rep(1, 15), rep(0, 12), rep(1, 4), rep(0, 6), rep(1, 6), 
                rep(0, 55), rep(1, 23), rep(0, 18), rep(1, 6), rep(0, 9), rep(1, 9), 
                rep(0, 49), rep(1, 29), rep(0, 16), rep(1, 8), rep(0, 7), rep(1, 11), 
                rep(0, 72), rep(1, 45), rep(0, 23), rep(1, 13), rep(0, 10), rep(1, 17)))